On the ratio of mixing length to scale height in red dwarfs

Cox, A. N.; Hodson, S. W.; Shaviv, G.

doi:10.1086/183517

Cited by 33 publications

(30 citation statements)

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“…The decreased convection effectively leads to a lower value of the mixing-length parameter (see Tayler 1987), which explains the better fit to the radius of the secondary using the Baraffe et al (1998) models with ML ¼ 1:0 as opposed to those with the solar value of ML ¼ 1:9. Similar improvements in the fit to other low-mass stars using a reduced mixing-length parameter were also reported by Clausen et al (1999a) and in fact much earlier by Gabriel (1969) and Cox et al (1981).…”

Section: Comparison With Other Starssupporting

confidence: 86%

The Eclipsing Binary V1061 Cygni: Confronting Stellar Evolution Models for Active and Inactive Solar‐Type Stars

Torres

Lacy

Marschall

et al. 2006

ApJ

103

117

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We present spectroscopic and photometric observations of the eclipsing system V1061 Cyg (P ¼ 2:35 days). A third star is visible in the spectrum, and the system is a hierarchical triple. We combine the radial velocities for the three stars, times of eclipse, and intermediate astrometric data from the Hipparcos mission (abscissa residuals) to establish the elements of the outer orbit, which is eccentric and has a period of 15.8 yr. We determine accurate values for the masses, radii, and effective temperatures of the binary components: M Aa ¼ 1:282 AE 0:015 M , R Aa ¼ 1:615 AE 0:017 R , and T Aa eA ¼ 6180 AE 100 K for the primary (star Aa), and M Ab ¼ 0:9315 AE 0:0068 M , R Ab ¼ 0:974 AE 0:020 R , and T Ab eA ¼ 5300 AE 150 K for the secondary (Ab). The mass of the tertiary is determined to be M B ¼ 0:925 AE 0:036 M and its effective temperature is T B eA ¼ 5670 AE 150 K. Current stellar evolution models agree well with the properties of the primary but show a very large discrepancy in the radius of the secondary, in the sense that the predicted values are $10% smaller than observed (a $5 effect). In addition, the temperature is cooler than predicted, by some 200 K. These discrepancies are quite remarkable given that the star is only 7% less massive than the Sun, the calibration point of all stellar models. We identify the chromospheric activity as the likely cause of the effect. Inactive stars agree very well with the models, while active ones such as V1061 Cyg Ab appear systematically too large and too cool.

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Section: Comparison With Other Starssupporting

confidence: 86%

The Eclipsing Binary V1061 Cygni: Confronting Stellar Evolution Models for Active and Inactive Solar‐Type Stars

Torres

Lacy

Marschall

et al. 2006

ApJ

103

117

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“…The coevality is recovered adopting a significantly lower mixing-length value for the secondary stars. This is an expected behaviour since it is recognised that in active stars the dynamo-induced magnetic fields can suppress convection and produce starspots, causing differences in temperature and radii with respect to standard stellar models, which can be mimicked by a lower mixing-length value (Gabriel 1969;Cox et al 1981;Clausen et al 1999). It is, however, clear that further research is mandatory to determine the expected errors in the calibrated mixing length in a sound statistical way.…”

Section: The Coevality Problem: a Statistical Approachmentioning

confidence: 96%

Grid-based estimates of stellar ages in binary systems

Valle

Dell’Omodarme

Moroni

et al. 2015

A&A

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Aims. We investigate the performance of grid-based techniques in estimating the age of stars in detached eclipsing binary systems. We evaluate the precision of the estimates due to the uncertainty in the observational constraints -masses, radii, effective temperatures, and [Fe/H] -and the systematic bias caused by the uncertainty in convective core overshooting, element diffusion, mixing-length value, and initial helium content. Methods. We adopted the SCEPtER grid, which includes stars with mass in the range [0.8; 1.6] M and evolutionary stages from the zero-age main sequence to the central hydrogen depletion. Age estimates have been obtained by a generalisation of the maximum likelihood technique described in our previous work. Results. We showed that the typical 1σ random error in age estimates -due only to the uncertainty affecting the observational constraints -is about ±7%, which is nearly independent of the masses of the two stars. However, such an error strongly depends on the evolutionary phase and becomes larger and asymmetric for stars near the zero-age main sequence where it ranges from about +90% to −25%. The systematic bias due to the including convective core overshooting -for mild and strong overshooting scenariosis about 50% and 120% of the error due to observational uncertainties. A variation of ±1 in the helium-to-metal enrichment ratio ΔY/ΔZ accounts for about ±150% of the random error. The neglect of microscopic diffusion accounts for a bias of about 60% of the error due to observational uncertainties. We also introduced a statistical test of the expected difference in the recovered age of two coeval stars in a binary system. We find that random fluctuations within the current observational uncertainties can lead genuine coeval binary components to appear to be non-coeval with a difference in age as high as 60%.

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“…In an early attempt to do ‘precision modelling’ of M dwarfs with inclusion of magnetic fields, Cox, Shaviv & Hodson (1981) reported on a fit to the then‐known parameters of the star Kruger 60A. This is a member of a binary which also includes the first flare star to have a known mass (Kruger 60B = DO Cep, with a mass of 0.14 M ⊙ : Van de Kamp & Lippincott 1951).…”

Section: Previous Modelsmentioning

confidence: 99%

Precision modelling of M dwarf stars: the magnetic components of CM Draconis

MacDonald

Mullan

2012

Monthly Notices of the Royal Astronomical Society

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The eclipsing binary CM Draconis (CM Dra) contains two nearly identical red dwarfs of spectral class dM4.5. The masses and radii of the two components have been reported with unprecedentedly small statistical errors: for M, these errors are 1 part in 260, while for R, the errors reported by Morales et al. are 1 part in 130. When compared with standard stellar models with appropriate mass and age (≈4 Gyr), the empirical results indicate that both components are discrepant from the models in the following sense: the observed stars are larger in R (‘bloated’), by several standard deviations, than the models predict. The observed luminosities are also lower than the models predict. Here, we attempt at first to model the two components of CM Dra in the context of standard (non‐magnetic) stellar models using a systematic array of different assumptions about helium abundances (Y), heavy element abundances (Z), opacities and mixing length parameter (α). We find no 4‐Gyr‐old models with plausible values of these four parameters that fit the observed L and R within the reported statistical error bars. However, CM Dra is known to contain magnetic fields, as evidenced by the occurrence of star‐spots and flares. Here we ask: can inclusion of magnetic effects into stellar evolution models lead to fits of L and R within the error bars? Morales et al. have reported that the presence of polar spots results in a systematic overestimate of R by a few per cent when eclipses are interpreted with a standard code. In a star where spots cover a fraction f of the surface area, we find that the revised R and L for CM Dra A can be fitted within the error bars by varying the parameter α. The latter is often assumed to be reduced by the presence of magnetic fields, although the reduction in α as a function of B is difficult to quantify. An alternative magnetic effect, namely inhibition of the onset of convection, can be readily quantified in terms of a magnetic parameter δ≈B2/4πγpgas (where B is the strength of the local vertical magnetic field). In the context of δ models in which B is not allowed to exceed a ‘ceiling’ of 106 G, we find that the revised R and L can also be fitted, within the error bars, in a finite region of the f–δ plane. The permitted values of δ near the surface leads us to estimate that the vertical field strength on the surface of CM Dra A is about 500 G, in good agreement with independent observational evidence for similar low‐mass stars. Recent results for another binary with parameters close to those of CM Dra suggest that metallicity differences cannot be the dominant explanation for the bloating of the two components of CM Dra.

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On the ratio of mixing length to scale height in red dwarfs

Cited by 33 publications

References 0 publications

The Eclipsing Binary V1061 Cygni: Confronting Stellar Evolution Models for Active and Inactive Solar‐Type Stars

The Eclipsing Binary V1061 Cygni: Confronting Stellar Evolution Models for Active and Inactive Solar‐Type Stars

Grid-based estimates of stellar ages in binary systems

Precision modelling of M dwarf stars: the magnetic components of CM Draconis

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